Question

on a particular day, the wind added 4 miles per hour to jamies rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her trip. jamie found that in the same amount of time she could row 54 miles with the wind, she could go only 30 miles against the wind. what is her normal rowing speed with no wind

Answer 1

Given: jamie found that in the same amount of time she could row 54 miles with the wind, she could go only 30 miles against the wind.

Let's assume Jamie's normal rowing speed = X mph.

It says the wind added 4 miles per hour to jamies rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip.

So her speed with wind = (x+4) mph

and her speed against wind = (x-4) mph

We know the formula of time = distance/speed

And time is same for both the trips:-

`(54)/(x+4) = (30)/(x-4)\\ \\ Cross\;\; multiplying\\\\54(x-4)=30(x+4)\\54x-216=30x+120\\54x-30x=120+216\\24x=336\\x=(336)/(24)=14\; mph`

So, Jamie's normal rowing speed = 14 mph

Answer 2

Let V be the Jamie speed without wind. When the wind added 4 miles per hour to Jamies rate when she was rowing with the wind, then her speed becomes V+4 and when the wind subtracted 4 miles per hour from her rate when she was rowing against the wind, then her speed becomes V-4.

Use formula S=V·t, where S is a distance, V - speed and t - time.

Jamie could row with the same time:

1. 54 miles with the wind, then 54=(V+4)·t;

2. 30 miles against the wind, then 30=(V-4)·t.

Express from each equation variable

t:
`t=(54)/(V+4) ,\\ \\ t=(30)/(V-4)`

and equate right sides of these equations.

`(54)/(V+4)=(30)/(V-4),\\ \\ 54(V-4)=30(V+4),\\ 54V-216=30V+120,\\54V-30V=120+216, \\ 24V=336, \\ \\ V=(336)/(24)=14`

Answer: The speed without wind is 14 miles per hour.